Summer Math Camp

You can apply for our 2020 Summer Camps Now and benefit from Super Early Bird Discounts!

Courses to be offered in 2020 Summer Math Camps

Improve School Math
– Transition to Algebra (Recommended for 4th, 5th and 6th Graders)
– Algebra-1 and Integrated Math-1 (Recommended for 8th and 9th Graders and advanced 7th Graders)
– Algebra-2 (Recommended for 10th graders and advanced 8th and 9th graders)

Go Beyond!
– Advanced Middle School Math with MathCounts/AMC 8-10 Problems (Recommended for advanced 6th, 7th and 8th Graders)
– Advanced High School Math with AMC 10/12 Problems (Recommended for advanced 9th, 10th and 11th Graders)
– Proof Mathematics with AIME Problems


CyberMath Academy offered a math camp at two locations in the summer of 2020:

Summer Math Camp Details
 

Dates: July 6– 18, 2020 (see calendar below for details please)

Location: Classes will be held at Harvard Law School, Wasserstein Hall, 1585 Massachusetts Ave, Cambridge, MA 02138.
Residential Students will stay at Harvard Square.

Ages: 11-18 for residential students, 9-18 for day students.

Tuition: $1,885 for day campers, $4,450 for residential students.

Please scroll down for more information.

Master Math in an Intensive Camp This Summer!

CyberMath Academy’s Summer Math Camp in Boston, MA is a selective summer program for students who would like to sharpen their math skills in the inspiring and motivating atmosphere of an Ivy League College. Our math camp provides a challenging environment in summer for students in which they master mathematics with the participation of brilliant students from all over the globe.

Advanced Math Program – Designed by Justin Stevens

“- Author of Olympiad Number Theory Through Challenging Problems Book

– “Our teacher, Justin, was a legend.” 2018 Camp Participant

– “Justin is a crazy good teacher and understands kids.” 2018 Camp Participant

– “Justin is the most awesome teacher EVER!!!’ 2018 Camp Participant”

    

“Math Olympiad Program – Designed by Evan Chen

– One of the coaches of the USA IMO Team

– Co-Exam Coordinator for the USA Olympiad Team Selection Tests

– Assistant Academic Director of the Math Olympiad Summer Program (MOP)

– Member of the USA Math Olympiad (USAMO) Committee”

 

Courses to Choose From and Who The Summer Math Camp is For

1- Students who would like to excel in school mathematics

Courses to choose from:

  • Advanced Middle School Math with MathCounts/AMC 8-10 Problems

    This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems at the level of or from MathCounts, AMC-8, AMC 10 and similar competitions. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers in our summer math camp and learn topics that are typically not covered at traditional school settings.

    Recommended Grade Levels: Although we do not limit students by grade level in our summer math camps, this course is typically recommended for students in grades 4th-8th.

    Course Description: This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.

    Contest Preparation: MathCounts, AMC 8, AMC 10.

    Course Objectives: As of the completion of the summer math camp, students will:

    1. Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.

    2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

    3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

    Teaching Philosophy: We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.

    Class Participation: Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.

    Curriculum: The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.

    Algebra

    • Ratios and Proportions
    • Algebraic Expressions
    • Linear Equations
    • Functions
    • Inequalities
    • Polynomial Expressions
    • Pascal’s Triangle
    • Binomial Theorem
    • Quadratic Equations

    Combinatorics

    • Counting
    • Statistics
    • Probability
    • Permutations
    • Combinations

    Number Theory

    • Divisibility
    • GCD and LCM
    • Prime Factorization
    • Radicals and Exponents
    • Modular Arithmetic
    • Sequences and Series
    • Gauss’s Formula

    Geometry

    • Angles
    • Triangles
    • Pythagorean Theorem
    • Polygons
    • Circles
    • Perimeter, Area and Volume
    • Coordinate Geometry
    • 3D Geometry

  • Advanced High School Math with AMC 10/12 Problems

    This course prepares students for American Mathematics Competitions 10 and 12 and the non-proof parts of AIME. The topics taught include the entire high school curriculum including trigonometry, advanced algebra, precalculus and advanced geometry, but exclude calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.

    Recommended Grade Levels: Although we do not limit students by grade level in our summer math camps, this course is typically recommended for advanced 7th and 8th graders and high school students.

    Course Description: This course will familiarize students with the essential concepts and techniques in Algebra II, PreCalculus, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.

    Contest Preparation: AMC 10/12, AIME, ARML, Mandelbrot, Purple Comet.

    Course Objectives: As of the completion of the summer math camp, students will:

    1. Have complete mastery of concepts covered in standard Algebra II and PreCalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).

    2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

    3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

    Teaching Philosophy: We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.

    Class Participation: Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.

    Curriculum: The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.

     

    Topics Covered In This Course

    Algebra

    – Quadratics/Discriminants & Conic Sections
    – System of Equations
    – Polynomial Division
    – Rational Root Theorem
    – Fundamental Theorem of Algebra
    – Vieta’s Formulas
    – Sequences and Series
    – Induction
    – Radicals and Rationalizing Denominators
    – Algebraic Factorizations
    – Complex Numbers
    – Inequalities
    – Functions
    – Exponents and Logarithms

    Combinatorics

    – Basic Counting: Constructive and Complimentary
    – Sets, Bijections, and Logic
    – Principle of Inclusion Exclusion
    – Combinations and Permutations
    – Pascal’s Triangle
    – Binomial Theorem
    – Combinatorial Identities
    – Pigeonhole Principle
    – Expected Value
    – Stars & Bars
    – Recursion
    – Fibonacci Numbers

    Number Theory

    – Prime Factorization
    – Divisibility Rules
    – Euclidean Algorithm
    – Diophantine Equations
    – Bezout’s Identity
    – Modular Arithmetic & Exponentiation
    – Fermat’s Little Theorem
    – Wilson’s Theorem
    – Chinese Remainder Theorem
    – Multiplicative Functions
    – Euler’s Theorem

    Geometry

    – Congruent & Similar Triangles
    – Special Parts of a Triangle
    – Triangle Area Formulas
    – Quadrilaterals
    – Angles in Polygons
    – Inscribed Angles in Circles
    – Power of a Point
    – Three-Dimensional Geometry
    – Trigonometry for Right Triangles
    – Unit Circle & Radians
    – Trigonometric Identities
    – Extended Law of Sines & Law of Cosines
    – Polar Coordinates & Geometry of Complex Numbers

    Click below to see sample lecture notes

    AUTHORS

    Justin Stevens: Accelerated Math Program Coordinator
    University of Alberta – jstevens@cybermath.academy – (909) 713-4398

    Forest Kobayashi: Curriculum Designer, Harvey Mudd College

    Alex Toller: Curriculum Designer

If you would like to get more information on AMC 8, 10, 12 and AIME competitions, please visit Mathematical Association of America’s American Mathematics Competitions (AMC) Page.

2- Students who would like to go above and beyond school mathematics

 

Courses to choose from:

– Proof Mathematics with AIME Problems

This course is a part of our Math Olympiad Program. You can find more information about our Math Olympiad Program below.

  • Math Olympiad Program Levels

    To find out what course is best for you at our summer math camp, please look at the information below:

    There are two tracks in this course:

    Proof Mathematics with AIME Problems For students who can comfortably qualify for the
    AIME and solve the first half of problems on the exam. These students might be
    aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.

    USA(J)MO: For students who can already comfortably qualify for USA(J)MO, and
    are aiming to score highly on it.

     

    First: Please determine your level below

    (1) Starting out on AMC, trying to qualify for AIME

    (2) Can solve 2 problems on AIME, hoping to solve 8

    (3) Can solve 6+ problems on AIME, hoping to solve 13

    (4) Can qualify for USA(J)MO, hoping to solve a problem or two

    (5) Can solve one or two USA(J)MO problems and solve hard USAJMO or medium USAMO problems

    (6) Aiming to solve the final P3 / P6 problems on USAMO
    Second:Learn about the tracks in our Math Olympiad Program

    Our Math Olympiad Program has two tracks:

    Entry Level Math Olympiad Course with Computations (Advanced AIME with Proofs)

    * Prerequisites: 6+ on AIME

    * Aiming for high AIME scores, and a couple problems on USA(J)MO

    Advanced Math Olympiad Course (USAJMO)

    * Prerequisites: consistently qualify for USA(J)MO

    * Aiming to score 14+ on USAMO

    Third: Placement

    – If you are in levels 1 or 2, you should sign up for our Advanced High School Math with AMC 10/12 Problems course. It covers AMC 10/12 and the non-proof problems on AIME.

    – If you are in levels 3 or 4, you should sign up for our Advanced AIME with Proofs course.

    – If you are in levels 5 or 6, you should sign up for our USA(J)MO course.

    Have questions? E-mail our Math Olympiad Program Coordinator Evan Chen at echen@cybermath.academy

  • Math Olympiad Program Curriculum

    There are two tracks in this program:

    Advanced AIME with Proofs: For students who can comfortably qualify for the
    AIME and solve the first half of problems on the exam. These students might be
    aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.

    USA(J)MO: For students who can already comfortably qualify for USA(J)MO, and
    are aiming to score highly on it.

    These two tracks overlap in any given year. The curriculum runs in a three-year cycle.

    Contest preparation: AIME, HMMT, USA(J)MO, IMO.

    Curriculum: The course operates on a three-year cycle, so students can repeat the course up to three times total, across both tracks. The summer math camp and year-round materials are disjoint.

    A detailed listing of topics covered appears below. Not all topics occur in all years. Most topics occur in multiple years, but they will have different examples and problems each time they appear over the three-year cycle.

    Each iteration of the course contains several practice exams.

    1- Topics appearing only in Advanced AIME with Proofs

    Algebra

    • Symmetric Polynomials. Vieta’s formulas, Newton sums, fundamental theorem of elementary symmetric polynomials.
    • Logarithms.Computational problems and equations involving logarithms.
    • Trig Equation. Algebraic problems involving trig functions.
    • Intro Functional Equation. Introduction to olympiad-style functional equations. Substitutions, injectivity and surjectivity, Cauchy’s functional equation.
    • Inequalities. Introduction to olympiad-style inequalities. AM-GM and Cauchy-Schwarz.

    Combinatorics

    • Computations with Probability. Random variables, expected value, linearity of expectation.
    • Enumeration. Computational counting problems.
    • Monovariants and Invariants. Finite processes.

    Geometry

    • Computational Geometry. AIME-style problems in Euclidean geometry.
      Angle Chasing.
    • Trig in Geometry.
    • Elementary Geometry. Angle chasing, power of a point, homothety.
    • Basics of Complex Numbers. Introduction to complex numbers in geometry.

    Number theory

    • Computations with Modular Arithmetic. Fermat, Wilson, Chinese Remainder theorem.
    • Diophantine Equations. Introduction to olympiad-style Diophantine equations.
    • Chinese Remainder Theorem.

    2- Topics appearing in both tracks

    Algebra

    • Generating Functions. Their uses in combinatorial sums.
    • Linear Recursions and Finite Differences.
    • Sums. Swapping order of summation.
    • Polynomials. Fundamental theorem of algebra, factorizations, roots.

    Combinatorics

    • Weights and Colorings.
    • Induction and Recursion.
    • Linearity of Expectation and Double-Counting.
    • Algorithms. Combinatorial problems involving discrete-time processes.
    • Graph Theory. Definitions and problems.
    • Ad-Hoc Constructions.
    • Problems on Rectangular Grids.

    Geometry

      • Power of a Point.
      • Homothety
      • Common Congurations.

    Number theory

        • Divisibility and Euclidean Algorithm. Bounding the remainders.
        • Look at the Exponent. p-adic evaluation, lifting the exponent.
        • Orders. Primes of the form a2 + b2. Primitive roots.

    3- Topics appearing only in USA(J)MO

    Algebra

        • Functional Equations. More diffi cult functional equations at the USAMO/IMO level.
        • Advanced Inequalities. Jensen and Schur. Fudging, smoothing.
        • Analysis and Calculus. Understanding the complete theorem statements in calculus and how they can be applied to olympiad problems. Differentiation and the relation
          to multiplicity of roots. Lagrange multipliers. Compactness.

    Combinatorics

        • Advanced Graph Theory. More di fficult olympiad problems involving graphs.
        • Advanced Algorithms.
        • Games and Processes.

    Geometry

        • Projective Geometry. Harmonic bundles, poles and polars.
        • Inversion.
        • Spiral Similarity.
        • Complex Numbers. Applications to problems.
        • Barycentric Coordinates. Applications to problems.

    Number theory

        • Constructions in Number Theory.
        • Integer Polynomials. Irreducibility, minimal polynomials, a taste of Galois theory.
        • Quadratic Reciprocity. Legendre symbols.

Summer Math Camp

Distribution of Math Strands

Morning Sessions: Combinatorics and Geometry topics will be covered.

Afternoon Sessions: Algebra and Number Theory topics will be covered.

 

Outstanding Teachers!

Please see our faculty page for our instructors. Summer Math Camp instructors will be some of the instructors listed on our faculty page or other outstanding teachers with similar credentials.

 

Guest Lectures by Harvard, MIT Researchers

TBA.

Students’ Forum

There will be two student forums for our students:

Students’ Forum 1: Learn how to get accepted to top colleges from students who currently attend Harvard, MIT and other top colleges.

Students’ Forum 2: Learn how to prepare for math competitions and olympiads from champions who aced these tests.

Harvard, MIT Campus Tours and Lab Visits

Harvard and MIT Campus Tours and laboratory visits are scheduled each year.

Sightseeing

We will visit the historical places to see first-hand where the United States was founded and learn about its history. Walk along The Freedom Trail, try many tastes at Quincy Market, when tired of walking hop on a Duck Tour and take a walk along Charles River. Feel smarter (pronounced SMAHTAH) at Harvard Square.

Schedule of Activities

DateMorningAfternoon
Sun, July 5Residential and Int. Students ArriveOrientation, Time at Harvard Square
Mon, July 6Opening,Placement Tests & Guest LectureMath Classes
Tue, July 7Math ClassesMath Classes
Wed, July 8Math ClassesMath Classes
Thu, July 9Math ClassesMath Classes
Fri, July 10Math ClassesMath Classes
Sat, July 11Harvard Campus Tour, Students’ ForumMIT Campus Tour
Sun, July 12Boston City Tour for Residential Students
Mon, July 13Math ClassesMath Classes
Tue, July 14Math ClassesMath Classes
Wed, July 15Math ClassesMath Classes
Thu, July 16Math ClassesMath Classes
Fri, July 17Math ClassesMath Classes
Sat, July 18Practice TestAward Ceremony
Domestic Residential Students Depart
Sun, July 19Academic Counseling for Int. StudentsStudy Planning for Int. Students
Mon, July 20International Students Depart

Daily Schedule

TimeActivityNotes
7:15 am – 8:15 amBreakfastResidential Students Only
8:15 am – 8:45 amDay students arrive
9:00 am – 12:15 pmMorning classes
12:15 pm – 1:15 pmLunch and Activity timeConversation with teachers/counselors
1:15 pm – 4:00 pmPractice Sessions
4:30 pm – 5:00 pmDay students depart
5:00 pm – 6:00 pmFree timeResidential Students Only*
6:00 pm – 7:15 pmDinnerResidential Students Only*
7:30 pm – 9:30 pmStudy TimeResidential Students Only*
9:30 pm – 10:30 pmFree TimeResidential Students Only
10:45 pmLights OutResidential Students Only

*Day students who wish to attend supervised evening recreational and academic activities at the residential program may do so for an additional fee. The cost will be $200 (including dinner and all activities).

Transportation to Summer Math Camp

Bus Service for Day Students

We offer bus transportation to our camp site if enough number of students sign up for our Summer Math Camp as day students from the cities listed below. Extra charge will apply and space is limited.

For day students, we provide buses from the following cities: Acton, Lexington, Weston, and Newton

Airport Pickup

Domestic residential and international students who will be staying with us overnight at our summer math camp are expected to arrive at Boston Logan International Airport or at the camp site between 7 am – 7 pm on July 5th. For tuition and fees, please see below.

Tuition and Deadlines

Tuition TypeDeadlineDay StudentResidential Student
Super Early BirdDecember 3rd$1,650$3,910
Early RegistrationJanuary 1st$1,885$4,450
Regular RegistrationApril 1st$1,985$4,700
Late RegistrationJune 1st$2,085$4,950
Super-Late RegistrationJuly 14th$2,185$5,150

Residential Tuition covers classes & teaching materials, activities, accommodation, meals and in-camp transportation.

Fees

International Students’ Fee: Additional $585.
Airport Pickup/Dropoff fee: $60 each
Lunch Fee for Day Students: $232 (Day Students might choose to bring their own lunch or purchase lunch at the University.)

You can save up to $790 by registering early!

Summer Math Camp Details
 
Dates: July 13–25, 2020 (see calendar below for details please)

Location: Classes will be held at Stanford University in Stanford, CA
Residential Students will stay in Silicon Valley.

Ages: 11-18 for residential students, 9-18 for day students.

Tuition: $1,885 for day campers, $4,450 for residential students.

Please scroll down for more information.

 

Master Math in an Intensive Camp This Summer!

CyberMath Academy’s Summer Math Camp in Silicon Valley is a selective summer program for students who would like to sharpen their math skills in the inspiring and motivating atmosphere of an Ivy League College. Our math camp provides a challenging environment in summer for students in which they master mathematics with the participation of brilliant students from all over the globe.

Dates

July 13–25, 2019 (see calendar below for details please)

Location

Classes will be held at: Stanford University

Students will stay in: Silicon Valley

 

Guest Lectures by Stanford Researchers

TBA.

Students’ Forum

Learn how to get accepted to top colleges from students who currently attend Stanford and other top colleges.

Stanford Campus Tour

Stanford Campus Tours and laboratory visits are scheduled each year.

Sightseeing

We will also see the beautiful San Francisco Bay Area. Our San Francisco tour includes Twin Peaks, Fisherman’s Wharf, Pier 39, Treasure Island, Golden Gate Bridge, Coit Tower and the yummy yummy Ghirardelli Chocolate Factory.

Advanced Math Program – Designed by Justin Stevens

“- Author of Olympiad Number Theory Through Challenging Problems Book

– “Our teacher, Justin, was a legend.” 2018 Camp Participant

– “Justin is a crazy good teacher and understands kids.” 2018 Camp Participant

– “Justin is the most awesome teacher EVER!!!’ 2018 Camp Participant”

    

Math Olympiad Program – Designed by Evan Chen

“- One of the coaches of the USA IMO Team

– Co-Exam Coordinator for the USA Olympiad Team Selection Tests

– Assistant Academic Director of the Math Olympiad Summer Program (MOP)

– Member of the USA Math Olympiad (USAMO) Committee”

 

Courses to Choose From and Who The Summer Math Camp is For

1- Students who would like to excel in school mathematics

Courses to choose from:

  • Advanced Middle School Math with MathCounts/AMC 8-10 Problems

    This course covers the main topics in middle school math. Students will be mastering these topics while solving challenging problems at the level of or from MathCounts, AMC-8, AMC 10 and similar competitions. Students go above and beyond Common Core standards in this brain-stimulating course. Students will also solve mathematical puzzles and cyphers in our summer math camp and learn topics that are typically not covered at traditional school settings.

    Recommended Grade Levels: Although we do not limit students by grade level in our summer math camps, this course is typically recommended for students in grades 4th-8th.

    Course Description: This course will familiarize students with the essential concepts and techniques in Pre-Algebra, Algebra I, Geometry, Number Theory and Combinatorics. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.

    Contest Preparation: MathCounts, AMC 8, AMC 10.

    Course Objectives: As of the completion of the summer math camp, students will:

    1. Have complete mastery of concepts covered in standard Pre-Algebra, Algebra I and Geometry courses, as well as topics not covered in traditional school curriculum.

    2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

    3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

    Teaching Philosophy: We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.

    Class Participation: Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.

    Curriculum: The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.

    Algebra

    • Ratios and Proportions
    • Algebraic Expressions
    • Linear Equations
    • Functions
    • Inequalities
    • Polynomial Expressions
    • Pascal’s Triangle
    • Binomial Theorem
    • Quadratic Equations

    Combinatorics

    • Counting
    • Statistics
    • Probability
    • Permutations
    • Combinations

    Number Theory

    • Divisibility
    • GCD and LCM
    • Prime Factorization
    • Radicals and Exponents
    • Modular Arithmetic
    • Sequences and Series
    • Gauss’s Formula

    Geometry

    • Angles
    • Triangles
    • Pythagorean Theorem
    • Polygons
    • Circles
    • Perimeter, Area and Volume
    • Coordinate Geometry
    • 3D Geometry

  • Advanced High School Math with AMC 10/12 Problems

    This course prepares students for American Mathematics Competitions 10 and 12 and the non-proof parts of AIME. The topics taught include the entire high school curriculum including trigonometry, advanced algebra, precalculus and advanced geometry, but exclude calculus. Our curriculum also includes some additional challenging and brain-stimulating topics outside of the traditional school curriculum.

    Recommended Grade Levels: Although we do not limit students by grade level in our summer math camps, this course is typically recommended for advanced 7th and 8th graders and high school students.

    Course Description: This course will familiarize students with the essential concepts and techniques in Algebra II, PreCalculus, Combinatorics, Number Theory, and Geometry. We will have a specific emphasis on problem solving where the students will constantly be challenged to think creatively.

    Contest Preparation: AMC 10/12, AIME, ARML, Mandelbrot, Purple Comet.

    Course Objectives: As of the completion of the summer math camp, students will:

    1. Have complete mastery of concepts covered in standard Algebra II and PreCalculus courses, as well as more advanced topics (such as Vieta’s formulas, Complex Numbers, and manipulation of Series).

    2. Be able to explain and employ important theorems and techniques used in Combinatorics, Number Theory, and Geometry.

    3. Be able to reduce unfamiliar problems to basic principles, and cleverly employ techniques they’ve learned to find shortcuts in solution methods.

    Teaching Philosophy: We believe that building good problem-solving skills is as (if not more) important than knowing lots of theorems. As such, although the course will cover a considerable amount of material, the main emphasis will be on building problem-solving intuition and training students to think creatively when faced with classes of problems they’ve never seen before.

    Class Participation: Students are expected to actively participate in class. We will employ the Socrates method, which is a cooperative dialogue between the students and teacher to stimulate critical thinking. Students will also collaborate with classmates while solving challenging problems.

    Curriculum: The course curriculum is owned and copyright by CyberMath Academy. The class material is composed of unique blends of problems hand picked from prestigious competitions from around the globe, along with many historical problems and fascinating puzzles.

     

    Topics Covered In This Course

    Algebra

    – Quadratics/Discriminants & Conic Sections
    – System of Equations
    – Polynomial Division
    – Rational Root Theorem
    – Fundamental Theorem of Algebra
    – Vieta’s Formulas
    – Sequences and Series
    – Induction
    – Radicals and Rationalizing Denominators
    – Algebraic Factorizations
    – Complex Numbers
    – Inequalities
    – Functions
    – Exponents and Logarithms

    Combinatorics

    – Basic Counting: Constructive and Complimentary
    – Sets, Bijections, and Logic
    – Principle of Inclusion Exclusion
    – Combinations and Permutations
    – Pascal’s Triangle
    – Binomial Theorem
    – Combinatorial Identities
    – Pigeonhole Principle
    – Expected Value
    – Stars & Bars
    – Recursion
    – Fibonacci Numbers

    Number Theory

    – Prime Factorization
    – Divisibility Rules
    – Euclidean Algorithm
    – Diophantine Equations
    – Bezout’s Identity
    – Modular Arithmetic & Exponentiation
    – Fermat’s Little Theorem
    – Wilson’s Theorem
    – Chinese Remainder Theorem
    – Multiplicative Functions
    – Euler’s Theorem

    Geometry

    – Congruent & Similar Triangles
    – Special Parts of a Triangle
    – Triangle Area Formulas
    – Quadrilaterals
    – Angles in Polygons
    – Inscribed Angles in Circles
    – Power of a Point
    – Three-Dimensional Geometry
    – Trigonometry for Right Triangles
    – Unit Circle & Radians
    – Trigonometric Identities
    – Extended Law of Sines & Law of Cosines
    – Polar Coordinates & Geometry of Complex Numbers

    Click below to see sample lecture notes

    AUTHORS

    Justin Stevens: Accelerated Math Program Coordinator
    University of Alberta – jstevens@cybermath.academy – (909) 713-4398

    Forest Kobayashi: Curriculum Designer, Harvey Mudd College

    Alex Toller: Curriculum Designer

If you would like to get more information on AMC 8, 10, 12 and AIME competitions, please visit Mathematical Association of America’s American Mathematics Competitions (AMC) Page.

2- Students who would like to go above and beyond school mathematics

Courses to choose from:

– Proof Mathematics with AIME Problems

This course is a part of our Math Olympiad Program. You can find more information about our Math Olympiad Program below.

  • Math Olympiad Program Levels

    To find out what course is best for you at our summer math camp, please look at the information below:

    There are two tracks in this course:

    Proof Mathematics with AIME Problems For students who can comfortably qualify for the
    AIME and solve the first half of problems on the exam. These students might be
    aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.

    USA(J)MO: For students who can already comfortably qualify for USA(J)MO, and
    are aiming to score highly on it.

     

    First: Please determine your level below

    (1) Starting out on AMC, trying to qualify for AIME

    (2) Can solve 2 problems on AIME, hoping to solve 8

    (3) Can solve 6+ problems on AIME, hoping to solve 13

    (4) Can qualify for USA(J)MO, hoping to solve a problem or two

    (5) Can solve one or two USA(J)MO problems and solve hard USAJMO or medium USAMO problems

    (6) Aiming to solve the final P3 / P6 problems on USAMO
    Second:Learn about the tracks in our Math Olympiad Program

    Our Math Olympiad Program has two tracks:

    Entry Level Math Olympiad Course with Computations (Advanced AIME with Proofs)

    * Prerequisites: 6+ on AIME

    * Aiming for high AIME scores, and a couple problems on USA(J)MO

    Advanced Math Olympiad Course (USAJMO)

    * Prerequisites: consistently qualify for USA(J)MO

    * Aiming to score 14+ on USAMO

    Third: Placement

    – If you are in levels 1 or 2, you should sign up for our Advanced High School Math with AMC 10/12 Problems course. It covers AMC 10/12 and the non-proof problems on AIME.

    – If you are in levels 3 or 4, you should sign up for our Advanced AIME with Proofs course.

    – If you are in levels 5 or 6, you should sign up for our USA(J)MO course.

    Have questions? E-mail our Math Olympiad Program Coordinator Evan Chen at echen@cybermath.academy

  • Math Olympiad Program Curriculum

    There are two tracks in this program:

    Advanced AIME with Proofs: For students who can comfortably qualify for the
    AIME and solve the first half of problems on the exam. These students might be
    aiming to qualify for USA(J)MO and have a pleasant start on the olympiad.

    USA(J)MO: For students who can already comfortably qualify for USA(J)MO, and
    are aiming to score highly on it.

    These two tracks overlap in any given year. The curriculum runs in a three-year cycle.

    Contest preparation: AIME, HMMT, USA(J)MO, IMO.

    Curriculum: The course operates on a three-year cycle, so students can repeat the course up to three times total, across both tracks. The summer math camp and year-round materials are disjoint.

    A detailed listing of topics covered appears below. Not all topics occur in all years. Most topics occur in multiple years, but they will have different examples and problems each time they appear over the three-year cycle.

    Each iteration of the course contains several practice exams.

    1- Topics appearing only in Advanced AIME with Proofs

    Algebra

    • Symmetric Polynomials. Vieta’s formulas, Newton sums, fundamental theorem of elementary symmetric polynomials.
    • Logarithms.Computational problems and equations involving logarithms.
    • Trig Equation. Algebraic problems involving trig functions.
    • Intro Functional Equation. Introduction to olympiad-style functional equations. Substitutions, injectivity and surjectivity, Cauchy’s functional equation.
    • Inequalities. Introduction to olympiad-style inequalities. AM-GM and Cauchy-Schwarz.

    Combinatorics

    • Computations with Probability. Random variables, expected value, linearity of expectation.
    • Enumeration. Computational counting problems.
    • Monovariants and Invariants. Finite processes.

    Geometry

    • Computational Geometry. AIME-style problems in Euclidean geometry.
      Angle Chasing.
    • Trig in Geometry.
    • Elementary Geometry. Angle chasing, power of a point, homothety.
    • Basics of Complex Numbers. Introduction to complex numbers in geometry.

    Number theory

    • Computations with Modular Arithmetic. Fermat, Wilson, Chinese Remainder theorem.
    • Diophantine Equations. Introduction to olympiad-style Diophantine equations.
    • Chinese Remainder Theorem.

    2- Topics appearing in both tracks

    Algebra

    • Generating Functions. Their uses in combinatorial sums.
    • Linear Recursions and Finite Differences.
    • Sums. Swapping order of summation.
    • Polynomials. Fundamental theorem of algebra, factorizations, roots.

    Combinatorics

    • Weights and Colorings.
    • Induction and Recursion.
    • Linearity of Expectation and Double-Counting.
    • Algorithms. Combinatorial problems involving discrete-time processes.
    • Graph Theory. Definitions and problems.
    • Ad-Hoc Constructions.
    • Problems on Rectangular Grids.

    Geometry

      • Power of a Point.
      • Homothety
      • Common Congurations.

    Number theory

        • Divisibility and Euclidean Algorithm. Bounding the remainders.
        • Look at the Exponent. p-adic evaluation, lifting the exponent.
        • Orders. Primes of the form a2 + b2. Primitive roots.

    3- Topics appearing only in USA(J)MO

    Algebra

        • Functional Equations. More diffi cult functional equations at the USAMO/IMO level.
        • Advanced Inequalities. Jensen and Schur. Fudging, smoothing.
        • Analysis and Calculus. Understanding the complete theorem statements in calculus and how they can be applied to olympiad problems. Differentiation and the relation
          to multiplicity of roots. Lagrange multipliers. Compactness.

    Combinatorics

        • Advanced Graph Theory. More di fficult olympiad problems involving graphs.
        • Advanced Algorithms.
        • Games and Processes.

    Geometry

        • Projective Geometry. Harmonic bundles, poles and polars.
        • Inversion.
        • Spiral Similarity.
        • Complex Numbers. Applications to problems.
        • Barycentric Coordinates. Applications to problems.

    Number theory

        • Constructions in Number Theory.
        • Integer Polynomials. Irreducibility, minimal polynomials, a taste of Galois theory.
        • Quadratic Reciprocity. Legendre symbols.

Summer Math Camp

Distribution of Math Strands

Morning Sessions: Combinatorics and Geometry topics will be covered.

Afternoon Sessions: Algebra and Number Theory topics will be covered.

 

Outstanding Teachers!

Please see our faculty page for our instructors. Summer Math Camp instructors will be some of the instructors listed on our faculty page or other outstanding teachers with similar credentials.

 

Schedule of Activities

DateMorningAfternoon
Sun, July 14Residential and Int. Students ArriveOrientation
Mon, July 15Opening,Placement Tests & Guest LectureMath Classes
Tue, July 16Math ClassesMath Classes
Wed, July 17Math ClassesMath Classes
Thu, July 18Math ClassesMath Classes
Fri, July 19Math ClassesMath Classes
Sat, July 20Math ClassesMath Classes
Sun, July 21San Francisco Tour***San Francisco Tour***
Mon, July 22Math ClassesMath Classes
Tue, July 23Math ClassesMath Classes
Wed, July 24Math ClassesMath Classes
Thu, July 25Math ClassesMath Classes
Fri, July 26Math ClassesMath Classes
Sat, July 27Practice TestAward Ceremony, Stanford Campus Tour
Sun, July 28Domestic Residential Students DepartAcademic Counseling, Study Planning
Mon, July 29International Students Depart

* For residential students. Day students can join with a $100 fee.

Daily Schedule

TimeActivityNotes
7:00 am – 7:30 amBreakfastResidential Students Only
8:00 am – 8:30 amDay Students Arrive
8:30 am – 11:30 pmMorning Classes
11:30 pm – 12:15 pmLunch and Activity TimeConversation with Teachers/Counselors
12:15 pm – 3:30 pmAfternoon Classes
3:30 pm – 4:00 pmSnack
4:00 pm – 5:00 pmDay Students Depart
5:00 pm – 6:00 pmOptional Study / Free TimeResidential Students Only*
6:00 pm – 7:15 pmDinnerResidential Students Only*
7:30 pm – 9:30 pmStudy TimeResidential Students Only*
9:30 pm – 10:30 pmFree TimeResidential Students Only
10:45 pmLights OutResidential Students Only

*Day students who wish to attend supervised evening recreational and academic activities at the residential program may do so for an additional fee. The cost will be $200 (including dinner and all activities).

Transportation to Summer Math Camp

Bus Service for Day Students

We offer bus transportation to our camp site if enough number of students sign up for our Summer Math Camp as day students from the cities listed below. Extra charge will apply and space is limited.

For day students, we provide buses from the following cities: Cupertino, Sunnyvale, Mountain View and Fremont.

Airport Pickup

Domestic residential and international students who will be staying with us overnight at our summer math camp are expected to arrive at a San Francisco Bay Area airport (San Francisco, San Jose or Oakland) or at the camp site between 7 am – 7 pm on July 14th. For tuition and fees, please see below.

Tuition and Deadlines

Tuition TypeDeadlineDay StudentResidential Student
Super Early BirdDecember 3rd$1,650$3,910
Early RegistrationJanuary 1st$1,885$4,450
Regular RegistrationJune 1st$1,985$4,700
Late RegistrationJune 1st$2,085$4,950
Super-Late RegistrationJuly 14th$2,185$5,150

Residential Tuition covers classes & teaching materials, activities, accommodation, meals and in-camp transportation.

Fees

International Students’ Fee: Additional $585.
Airport Pickup/Dropoff fee: $60 each
Lunch Fee for Day Students: $232 (Day Students might choose to bring their own lunch or purchase lunch at the University.)

You can save up to $790 by registering early!

Admissions and Placement

Please fill out the form below to apply. Please provide as much detailed information on the student’s background as possible:

Background Information (not required for returning students): Please provide the student’s background. Please include student’s academic achievements, GPA, any Honors or AP Courses taken, competition experience, any year-round or summer advanced courses/camps that the student has participated in.

We will get back to you with an admission decision and payment details if the student is admitted. All students will take a placement test on the first instructional day of our summer camps and will be assigned to their appropriate groups. We continuously monitor our students’ progress throughout the camp and make adjustments to their assignments when necessary. If you would like to discuss your child’s placement, please do not hesitate to give us a call or email us at info@cybermath.academy

Summer Math Camp Application

* This event is not owned, controlled, supervised or sponsored by Harvard University or any of its schools or programs.

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